He’s a three-time accused rapist who once faced up to 75 years in jail — and now he wants the city to fork over $3 million for the couple of extra months he spent in the slammer as the cases against him fell apart.

Brian Brockington — who skated on the violent rape charges after Bronx prosecutors bungled the case — has filed a notice of claim, the first step toward a lawsuit, against the city and its Department of Correction.

The 36-year-old became the poster boy for ineptitude at Bronx District Attorney Robert Johnson’s office after he walked out of Rikers Island a free man in May, even though authorities said he was linked by DNA to violent sex attacks in 1993, 1997 and 2003.

Brockington’s lawsuit will contend that he was kept behind bars just over 100 days longer than he should have been after he struck a plea deal in the 2003 case, as the 1993 and 1997 cases fell apart, sources told The Post.

The debacle started in 2007, when Brockington was first picked up on an unrelated matter and cops got a DNA swab from him.

That sample allegedly linked him to the Dec. 5, 1993, gunpoint rape of a 28-year-old woman at a Bronx playground, the 1997 rape of a prostitute on a Story Avenue rooftop, and a 2003 attack on a woman at a Soundview party.

After Brockington’s arrest, prosecutors learned that the rape kit from the 1993 crime wasn’t tested until 2002 because of a lab backup. On Dec. 4, 2003 — one day before the 10-year statute of limitations ran out — Bronx prosecutors got an indictment of the then-“John Doe” rapist.

But prosecutors didn’t file charges until Dec. 6, 2003, one day too late.

It wasn’t until February 2010 that the Bronx DA’s Office realized the mistake and was forced to drop those charges.

The 1997 case also wound up being dropped because of “evidentiary problems” that the DA declined to disclose.

That left prosecutors with only the 2003 case against Brockington — who cut a plea deal that reduced the charge to attempted assault and carried a 1 1/2- to 4-year sentence.

By the time he was sprung from Rikers in May, Brockington had served longer than that.

“Corrections did not take into consideration the five years he spent in jail. They just ignored it,” a source said. “There’s no question they dropped the ball. They just sat on it; he should have been released.”